Pseudospectra of elements of reduced Banach algebras II

Krishnan, Arundhathi; Kulkarni, S. H.

Pseudospectra of elements of reduced Banach algebras II

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9044_158-978-1-PB.pdf(210.2 KB)

Published version

Date

2018

Authors

Krishnan, Arundhathi

Kulkarni, S. H.

Publisher

Univerzitet u Nišu, University of Nis, Serbia

Abstract

Let A be a Banach algebra with identity 1 and p ∈ A be a non-trivial idempotent. Then q = 1 − p is also an idempotent. The subalgebras pAp and qAq are Banach algebras, called reduced Banach algebras, with identities p and q respectively. Let x ∈ A be such that pxp = xp, and ε > 0. We examine the relationship between the spectrum of x ∈ A, σ(A, x), and the spectra of pxp ∈ pAp, σ(pAp, pxp) and qxq ∈ qAq, σ(qAq, qxq). Similarly, we examine the relationship betweeen the ε-pseudospectrum of x ∈ A, Λε(A, x) and ε-pseudospectra of pxp ∈ pAp, Λε(pAp, pxp) and of qxq ∈ qAq, Λε(qAq, qxq).

Keywords

Banach algebra , Direct sum , Idempotent , Pseudospectrum , Reduced Banach algebra , Spectrum

Citation

A. Krishnan and S. H. Kulkarni (2018) 'Pseudospectra of elements of reduced Banach algebras II'. Functional Analysis, Approximation and Computation, 10(2), pp. 33-45.